Dynamics of a vibro-impact self-propelled capsule encountering a circular fold in the small intestine

Given the anatomy of the small intestine, this paper investigates the dynamics of a vibro-impact capsule moving on an intestinal substrate with the consideration of a circular fold which provides the main resistance for the capsule’s progression. To this end, a new mathematical model of the capsule-fold contact that can depict the entire procedure of fold crossing is proposed. Our bifurcation analyses suggest that the capsule always performs period-1 motion when the driving force is small, and fold crossing requires a large excitation amplitude, especially when the duty cycle ratio is small. By contrast, the excitation period of the capsule does not have a strong influence on fold crossing. It is found that the inner mass, capsule mass, frictional coefficient and fold’s height have a significant influence on capsule’s crossing motion. We also realise that Young’s modulus of the tissue has a critical influence on the bifurcation pattern of the capsule, where a stiffer tissue may lead to the co-existence of three stable attractors. On the contrary, the capsule’s length and stiffness of the impact springs have less influence on the capsule’s dynamics. The findings of this study can help with the optimisation and control of capsule’s locomotion in the small intestine.